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The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if sigma(n)=kn for some integer k>2, where sigma(n) is the divisor function. The ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

A set of real numbers x_1, ..., x_n is said to possess an integer relation if there exist integers a_i such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. For ...